An efficient immersed boundary-lattice Boltzmann flux solver for simulation of 3D incompressible flows with complex geometry

Abstract

To effectively simulate flows with complex geometry on stretched Cartesian grids, an efficient three-dimensional (3D) immersed boundary-lattice Boltzmann flux solver (IB-LBFS) is presented in this work. In the solver, the flow field is obtained by using the finite-volume LBFS, which applies the standard lattice Boltzmann method locally to reconstruct both viscous and inviscid fluxes simultaneously at each cell interface. The no-slip boundary condition is implemented by using an implicit boundary condition-enforced immersed boundary method. As a consequence, the IB-LBFS effectively combines the desirable features of the lattice Boltzmann flux solver and the immersed boundary method. As compared with conventional immersed boundary-lattice Boltzmann method (LBM) for applications on non-uniform grids, the tedious computation and storage of a large number of algebraic coefficients [11] are completely removed in the present solver. The proposed solver is validated by simulating flows past a stationary sphere, torus with different aspect ratios and rotating spheres. The obtained results agree well with the published data. Numerical results also show that the present solver is able to improve the computational efficiency largely and, at the same time, reduce the required virtual memory substantially.